Line element in quantum gravity: the examples of DSR and noncommutative geometry

Abstract

We question the notion of line element in some quantum spaces that are expected to play a role in quantum gravity, namely non-commutative deformations of Minkowski spaces. We recall how the implementation of the Leibniz rule forbids to see some of the infinitesimal deformed Poincare transformations as good candidates for Noether symmetries. Then we recall the more fundamental view on the line element proposed in noncommutative geometry, and re-interprete at this light some previous results on Connes' distance formula.

some references added. Proceedings of the Second Workshop on Quantum Gravity and Noncommutative Geometry, Universidade Lusofona, Lisbon 22-24 September 2008

References in corpus (11)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Gravity coupled with matter and foundation of non-commutative geometry
• Gauge Theory on Noncommutative Spaces
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Doubly Special Relativity
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• A Farewell To Unimodularity
• A no-pure-boost uncertainty principle from spacetime noncommutativity
• Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory
• First results of the Noether theorem for Hopf-algebra spacetime symmetries

Cited by in corpus (4)

• On Pythagoras' theorem for products of spectral triples
• Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
• Noncommutative geometrical origin of the energy-momentum dispersion relation
• A dual formula for the spectral distance in noncommutative geometry